Quantitative predictors
Key topics to emphasise
- Clarify the meaning of partial regression coefficients as “holding other variables constant.”
- Discuss the role of centred and standardised predictors for interpretability and numerical stability.
Potential examples
- Fit a model predicting fuel efficiency (e.g.,
mtcars data) from engine size, weight, and horsepower to show competing effects.
- Contrast models with raw vs. centred predictors to illustrate interpretational differences.
Potential exercises
- interpret the coefficient of weight before and after centring.
- build a scatterplot matrix to hypothesise relationships among continuous predictors before modelling.
Multi-collinearity
Key topics to emphasise
- Define variance inflation factors (VIFs) and tolerance as diagnostic tools.
- Explain why multicollinearity inflates standard errors and complicates inference.
- Highlight remedial strategies: collecting more data, combining variables, or using regularisation methods.
Potential examples
- Demonstrate high correlation between horsepower and displacement in the
mtcars dataset and show the impact on coefficient estimates.
- Compare model outputs before and after removing a redundant predictor.
Potential exercises
- Provide correlation matrices and ask learners to flag problematic pairs of predictors.
- Have learners compute VIFs for a fitted model and interpret which predictors require attention.
Qualitative predictors
Key topics to emphasise
- Review dummy (indicator) coding and how the choice of reference category affects interpretation.
- Explain how to include categorical predictors with more than two levels using treatment or sum coding.
- Introduce the concept of adjusted means when controlling for other predictors.
Potential examples
- Model exam scores using study hours (continuous) and teaching method (categorical) to illustrate contrasts.
- Show how to interpret coefficients when switching the reference category.
Potential exercises
- Ask learners to encode a three-level categorical variable manually and verify with software output.
- Provide regression results and have learners translate coefficients into comparisons between categories.